Question

how many numbers are up to 150 are divisible by 9​

Answer 1

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Answer 2

Given,

Numbers from 1 to 150.

To find,

How many numbers are divisible by 9.

Solution,

• The smallest number from 1 to 150 that is divisible by 9 is ⇒ 9.

• The largest number from 1 to 150 that is divisible by 9 is ⇒

        Divide 150 by 9 and then subtract the remainder.

• So the largest number between 1 to 150 that is divisible by 9 is 144.

Therefore,

9,18,27,36,till144 are the numbers between 1 to 150 that are divisible by 9 and it is in Arithmetic Progression because there is a common difference of 9 between them.

To count the numbers of terms in 9,18,27,36 till 144 is-

an = a + (n-1)d

where an is the last term, a is the first term and d is the common difference between the term.

⇒   144 = 9 + (n-1)9

⇒   144 = 9 + 9n - 9

⇒   144 = 9n

⇒   n = 144/9

⇒   n = 16.

Hence, the numbers of terms up to 150 that are divisible by 9 are 16.